If a metal cube of side $5 \, cm$ has a charge of $6 \, \mu C$,then the surface charge density is

The figure shows a charged conductor resting on an insulating stand. If at point $P$ the charge density is $\sigma$,the potential is $V$,and the electric field strength is $E$,what are the values of these quantities at point $Q$?

Charges $Q, 2Q$ and $-Q$ are given to three concentric conducting shells $A, B$ and $C$ respectively as shown. The ratio of charges on the inner and outer surfaces of shell $C$ will be:

Electric charge is transferred to an irregular metallic disk as shown in the figure. If $\sigma_1, \sigma_2, \sigma_3$ and $\sigma_4$ are surface charge densities at the given points,then choose the correct answer from the options given below:

$A$ particle of mass $2 \times 10^{-6} \ kg$ with a charge $5 \times 10^{-6} \ C$ is hanging in air above a similarly charged conducting surface. The charge density of the surface is (Assume $\epsilon_0 = 8.85 \times 10^{-12} \ C^2 N^{-1} m^{-2}$ and $g = 10 \ m \ s^{-2}$)

Obtain the formula for the electric field due to a long thin wire of uniform linear charge density $\lambda$ without using Gauss's law.